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L p -solvability of the Dirichlet problem for the heat equation in noncylindrical domains with isolated characteristic points at the boundary

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We study the solvabitlity of the Dirichlet problem for the heat operator in weighted Sobolev L p -spaces in noncylindrical paraboloid type domains with isolated characteristic points at the boundary. For any p > 1 we find a necessary and sufficient L p -solvability condition and establish an L p -estimate. The results are formulated in terms of Muckenhoupt type conditions on the weight. Bibliography: 10 titles.

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Authors and Affiliations

  1. Vladimir State University, 87, ul. Gor’kogo, Vladimir, 600000, Russia

    Yu. A. Alkhutov & L. I. Kurlykova

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  1. Yu. A. Alkhutov
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  2. L. I. Kurlykova
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Correspondence to Yu. A. Alkhutov.

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Dedicated to V. V. Zhikov with great respect

Translated from Problems in Mathematical Analysis 58, June 2011, pp. 5–23.

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Alkhutov, Y.A., Kurlykova, L.I. L p -solvability of the Dirichlet problem for the heat equation in noncylindrical domains with isolated characteristic points at the boundary. J Math Sci 176, 710–731 (2011). https://doi.org/10.1007/s10958-011-0432-5

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  • DOI: https://doi.org/10.1007/s10958-011-0432-5

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